/*************************************************************************
 * File Name:    Minimum_Path_Sum.cc
 * Author:       zero91
 * Mail:         jianzhang9102@gmail.com
 * Created Time: 2013-11-8 16:47:37
 * 
 * Description:  
 |------------------------------------------------------------------------
 | Problem:Minimum Path Sum
 | Given a m x n grid filled with non-negative numbers, find a path from top
 | left to bottom right which minimizes the sum of all numbers along its path.
 |
 | Note: You can only move either down or right at any point in time.
 |------------------------------------------------------------------------
 ************************************************************************/

#include <iostream>
#include <algorithm>
#include <vector>
#include <queue>
#include <stack>
#include <deque>
#include <map>
#include <set>
#include <functional>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <cctype>
#include <cmath>

using namespace std;

class Solution {
public:
    int minPathSum(vector<vector<int> > &grid)
    {
        if (grid.size() == 0) return 0;
        
        int row = grid.size();
        int col = grid[0].size();
        int dp[row][col];
        
        dp[0][0] = grid[0][0];
        for (int i = 1; i < row; ++i) dp[i][0] = dp[i - 1][0] + grid[i][0];
        for (int i = 1; i < col; ++i) dp[0][i] = dp[0][i - 1]+ grid[0][i];
        
        for (int i = 1; i < row; ++i) {
            for (int j = 1; j < col; ++j) {
                dp[i][j] = min(dp[i - 1][j], dp[i][j - 1]) + grid[i][j];
            }
        }
        return dp[row - 1][col - 1];
    }
};

